- Email: [email protected]
Vapor-liquid equilibrium calculation of the system water-nitric acid over the entire concentration range
IUIIBPIM EOUIUBRll ELSEVIER
Fluid Phase Equilibria 114 (1996) 37-45
Vapor-liquid equilibrium calculation of the system water-nitric acid over the entire concentration range Stefano Brandani *, V i n c e n z o Brandani Dipartimento di Chimica, lngegneria Chimica e Materiali, Universith de L'Aquila, 1-67040 Monteluco di Roio, L'Aquila. Italy Received 1 February 1995; accepted 29 June 1995
Abstract
The vapor-liquid equilibrium of the system water-nitric acid has been described. The activity coefficients in the liquid phase are evaluated according to a new model. This model combines the effect of the long range forces expressed by a Debye-Hi~ckel contribution on a mole fraction basis, with the effect of short range forces expressed by a virial expansion of the NRTL equation. The proposed model can be used to describe the vapor-liquid equilibrium of the system water-nitric acid from 20 to 120 °C over the entire concentration range. Keywords: Theory; Application; Activity coefficients; Nitric acid
1. I n t r o d u c t i o n
The system water-nitric acid is important in industrial applications and environmental control (Tang et al., 1988). There is a considerable interest in the solubility of volatile strong electrolytes in atmospheric clouds and aerosol. Trace quantities of nitric acid are present in the atmosphere as a result of NO x oxidation. For this reason a model for the calculation of vapor-liquid equilibrium has to be capable of describing this system from the infinite dilution region to the pure liquid electrolyte. Clegg and Brimblecombe (1990) have shown that it is not necessary to introduce partial association even at high concentration of the electrolyte. A molal based extended Pitzer model can be applied up to a mole fraction of 0.3 (Brandani et al., 1994). To represent the entire concentration range it is necessary to use model based on mole fraction. Clegg and Brimblecombe (1990) have applied the mole fraction Pitzer model (Pitzer, 1991) up to a mole fraction of approximately 0.5. They have also proposed an extended model which covers the entire concentration range.
* Corresponding author. 0378-3812/96/Sl5.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0 3 7 8 - 3 8 1 2 ( 9 5 ) 0 2 8 1 8 - 8
38
S. Brandani, V. Brandani / Fluid Phase Equilibria 114 (1996) 37-45
In this contribution we propose a new model which retains Pitzer's expression for the Debye-Htickel effect and describes the short range interactions using the VNRTL55 model (Brandani et al., 1991).
2. Activity coefficients model Assuming complete dissociation of the electrolyte, the activity coefficient of the solvent and the mean activity coefficient of the acid are given by: In y, = (In "yl) DH
"t"
(ln
(l)
")/1) SR
In T+*= (ln y +, )~DH + (ln7_+) . SR
(2)
where according to Pitzer ( 1991 )
)DH (lny I
1)/2
=2Axl+pi~/2
2 (In Y_+) , , D n = _ a x P In(1 +
(3)
pilx/2) +
Ilx/2 - 2Ix~/z ] i +P/x--~
(4)
with
(5) p = 2287.66 - ~ I
(6)
2
(7)
I x = 7 . ~ z i Xi
where dw is the density of water (g cm-3). For the short range contribution we propose the use of the VNRTL55 equation (Brandani et al., 1991). This equation gives the activity coefficients from a virial expansion of the NRTL model about their infinite dilution values. Since the structure of the equation is in the form of a virial expansion, it can be easily applied to the water-nitric acid system. Therefore: (lnyl) sR=(lny;)sR+
5(1)
~ j=
5(1) Dj+x~
( l n y 2 ) sR= E j=l
~
~-" Dj, x i
(8)
(9)
S. Brandani, V. Brandani / Fluid Phase Equilibria 114 (1996) 37-45
39
where XH20
X1
(10)
XH~o + 2 XHNO3 (11)
XHNO"
X ±=
XH2O ~ 2XHNO~
where XHNO3 and XH20 are the apparent mole fractions of the electrolyte and water. Djj and Dj+ are the virial expansion coefficients which are dependent only on the NRTL model parameters. The analytical expressions for the first three coefficients are given by Brandani et al. (1991). The last two coefficients in the virial expansions are obtained imposing the boundary conditions. For the solvent the following equations are obtained: (lnYl) s~ + ~ j=
EJ
Dj, = 0
(12)
Dj,=0
(13)
i= while from the mean activity coefficient of the strong electrolyte the following equations can be derived: (In ~'sR + g5 ( 1 )
ln2=0
(14)
j=l
(15)
J7
i--t ~
3. V a p o r - l i q u i d equilibrium calculations
The vapor-liquid equilibrium for the water-nitric system acid is described by the following relationships: P,,~o =
"Y,xlpS~o
(16)
PItNO., = 'y+*2 X±/'/HNO3 2 ,,
(17)
with the assumption of ideal behavior in the vapor phase. The vapor pressure of pure water is taken from Saul and Wagner (1987), while the expression for the Henry constant of nitric acid is taken from Clegg and Brimblecombe (1990) and is given by: In HHNo,(bar) = -- 385.959036 +
3020.3522 T + 71.001998 In T - 0.131442311T
+ 0.420928363 • 10 -4 T 2
(18)
40
S. Brandani, V. Brandani/Fluid Phase Equilibria 114 (1996)37-45
The adjustable parameters in the model are the infinite dilution activity coefficients of the short range contribution, the two interaction parameters and the nonrandomness parameter. The temperature dependence of the first four parameters is obtained from thermodynamic considerations and is given by: (In y]c)SR = a0 + a,
(In
,y~_+)SR ~-
(1 1) T
b0 + bt T
r~+-=c°+cl
~'+-l -= d°-I- dl
T
(,
(19)
TO
(20)
TO
(21)
To
1)
T
(22)
To
Because of the physical meaning of the nonrandomness parameter a , we can suppose it to be a slowly increasing function of temperature. We have assumed a simple linear dependence given by: ,~ = 0.3 + f l ( T - To)
(23)
where TO = 298.15 K.
4. Results and discussion In order to determine the model parameters we have used the experimental isobaric data reported by Boublik and Kuchynka (1960). The measurements are at five different pressure levels 50, 100, 200, 400 and 760 Torr and vary from 24.6 to 120.6 °C over the entire concentration range. The objective function was defined as: N ~SQ
=
Y'. (Ti,ex p -
i=l
N Ti,ca,c)2 + W
Y'~ ( Y i . e x p - Yi,calc) 2
i=l
where N = 68 represents the number of experimental points and W, the ratio o-v2/O-y2, was set to 4- 10 4.
Table I Model parameters ao
-- 1.84___0.05
a1 bo b1 co c1 do dI fl × 104
- 1036+76 -3.12+0.02 - 1976+39 3.35 ___0.09 1189+31 - 2.88 _+ 0.05 - 1316_+41 25.5 + 3.6
S. Brandani, V. Brandani/Fluid Phase Equilihria 114 (1996)37-45
41
I-.-
I 2801 0.0
0.2
0.4
__ 06
_
_ 0.8
1.0
Mole fraction of nitric acid, x,y
Fig. I. Isobaric vapor-liquid equilibria for the system water-nitric acid. - - , calculated, experimental data: A, 50 Torr; *, 100 Torr; m, 200 Torr; x , 400 Tom D, 760 Torr (Boublik and Kuchynka, 1960).
The values of the parameters are reported in Table 1. The model is capable of representing the experimental data with an average absolute deviation (AAD) of 0.76 K on temperature and 0.013 on vapor composition. Fig. 1 shows the comparison between the isobaric experimental data (Boublik and Kuchynka, 1960) and model calculations. Fig. 2 shows the comparison between the isothermal experimental data (Perry and Chilton, 1973) and model calculations at three different isotherms. From these figures it can be seen that there is a very good agreement between the model calculations and the experimental data of Boublik and Kuchynka (1960), while the comparison with the data reported by Perry and Chilton (1973) can be considered satisfactory. The model accurately represents the azeotropic points.
700
~-
/ I
1
10o 0----0
02
04
0.6
0.8
I
Mote fractionof nitricacid, x,y Fig. 2. Isothermal vapor-liquid equilibria for the system water-nitric acid. - - , 25°C; g , 50°C; m, 75°C (Perry and Chilton, 1973).
calculated, experimental data: A,
42
S. Brandani, V. Brandani / Fluid Phase Equilibria 114 (1996) 37-45
1000 0
cl
IO0
el"
~/. 6"""~;J,'6"'"2Jd6"~;~'""3;65""~J:F6""~J4iS~;~5""~.8o
1000/T Fig. 3. Vapor pressure of pure nitric acid as a function of temperature. - - , present model; ---, Clegg and Brimblecombe (1990); D, Perry and Chilton (1973); zx, TRC Thermodynamic Tables (1987).
For the isothermal data, the largest deviations between experimental and calculated values occur at higher concentrations (XHNO3 > 0.7) and at higher temperatures. Since the accuracy of the experimental data reported by Perry and Chilton (1973) is not established, such deviations could be due to experimental uncertainty. In order to check the validity of this statement we carried out a comparison between vapor pressures of pure nitric acid calculated according to our model and those reported by Perry and Chilton (1973) and the more recent data of TRC Thermodynamic Tables (1987). Fig. 3 shows this comparison along with the vapor pressures calculated according to the model of Clegg and Brimblecombe (1990). It can be seen that especially at higher temperatures our model slightly overestimates the vapor pressures reported by TRC Thermodynamic Tables (1987), while there is a larger deviation with the data reported by Perry and Chilton (1973). Taking into account that even very small amounts of water will considerably lower the apparent vapor pressure of nitric acid, we consider the result obtained with our model to be acceptable. The predictions at higher temperatures obtained with the model of Clegg and Brimblecombe (1990) appear to be low, this can probably be ascribed to the fact that their model can be applied over a wider temperature range ( - 60-120 °C). Since Clegg and Brimblecombe (1990) have studied in detail the system water-nitric acid, we have carried out a comparison with their model on the vapor-liquid equilibrium calculations. Clegg and Brimblecombe (1990) use an extension of the model proposed by Pitzer (1991) to describe the entire concentration range. An explicit temperature dependence of the model parameters is not given. To obtain this information the activity coefficients are first evaluated at a reference temperature (25 °C) and then the solute and solvent activities can be calculated at any given temperature using the partial molal enthalpies and the partial molal heat capacities. The partial molal enthalpies are calculated using four sets of Chebyshev polynomials corresponding to four concentration intervals, while the partial molal heat capacities are expressed in the form of three sets of Chebyshev polynomials corresponding to three concentration intervals. The overall computational scheme is therefore more cumbersome. The model has been correlated to an extensive data base fitting 4 parameters at 25 °C
43
S. Brandani, V. Brandani / Fluid Phase Equilibria 114 (1996)37-45
Table 2 Comparison of differentmodels on isobaric experimental data (Boublik and Kuchynka, 1960)
Present model Clegg and Brimblecombe(1990)
AAD (68) a 7"(K)
y
0.76 2,90
0.013 0.035
Value in parenthesis is the number of data points.
Table 3 Comparison of differentmodels on isothermalexperimental data
Present model Clegg and Brimblecombe(1990)
Perry and Chilton(1973) AAD (Tort) Pn:o (260) a PHNO3 (260) a 5.81 7.89 6.98 10.9
Tang et al. (1988) AAD (Torr) P"2o (9) a PHNO3 (22) a 0.578 0.00113 0,027 0.00013
a Values in parenthesis are the number of data points. and a total of 96 coefficients of the Chebyshev polynomials. For this reason the Clegg and Brimblecombe model can be considered highly accurate. Table 2 reports the comparison between the two models applied to the isobaric experimental data of Boublik and Kuchynka (1960). Table 3 reports the comparison between the two models with the isothermal data given by Perry and Chilton (1973) and by Tang et al. (1988). The comparison shows that our model represents the system water-nitric acid over the entire concentration range with an accuracy comparable to that of Clegg and Brimblecombe (1990). The data of Tang et al. (1988) which are at low acid compositions (XHyo3 < 0.11) show that our model is less accurate in the dilute region. If very accurate evaluations are needed in this range of compositions either the Clegg and Brimblecombe model or the model of Brandani et al. (1994) should be used.
5. Conclusion We have presented a new model capable of representing the vapor-liquid equilibrium of the system water-nitric acid over the entire concentration range. An explicit temperature dependence has been given for each adjustable parameter which allows the vapor-liquid equilibrium calculations over the temperature range 20-120°C. For practical applications this model is more easily coded and has a simpler computational scheme than the model proposed by Clegg and Brimblecombe (1990).
6. List of symbols Ax dw
parameter defined by Eq. 5 density of water
44
S. Brandani. V. Brandani / Fluid Phase Equilibria 114 (1996) 37-45
Djl Dj + e
H Ix k
NA PHNO) °
T W x
Y
virial coefficients of the solvent virial coefficients of the mean activity coefficient electric charge Henry's constant ionic strength defined in Eq. 7 Boltzmann's constant Avogadro's number partial pressure of nitric acid partial pressure of water vapor pressure of pure component temperature weight in objective function (Eq. 24) mole fraction in the liquid phase mole fraction in the vapor phase
6.1.1. Greek letters o/ nonrandomness parameter activity coefficient of water Yl mean activity coefficient 3'_+ dielectric constant of water E parameter defined by Eq. 6 P interaction parameter of the NRTL equation ~u 6.1.2. Superscripts and subscripts DH Debye-HiJckel contribution HNO 3 nitric acid H 2° water SR short range contribution
Acknowledgements The authors are indebted to the italian Ministero dell'Universith e della Ricerca Scientifica e Tecnologica (MURST) for financial support.
References Boublik, T. and Kuchynka, K., 1960. Gleichgewicht Flussigkeit-Dampf XXII. Abhangigkeit der Zusammensetzung des Azeotropischen Gemisches des Systems Salpetersaure- Wasser vom Druck. Collect. Czech. Commun. 25: 579-582. Brandani, S., Brandani, V., Del Re, G. and Di Giacomo, G., 1991. Activity coefficients from a virial expansion about their infinite-dilution values. Chem. Eng. J., 46: 35-42. Brandani, S., Brandani, V. and Di Giacomo, G. 1994. Extended Pitzer Model for 1-1 Electrolyte Solutions: Ranges of Applicability from a Study of the System Water Nitric Acid. Chem. Biochem. Eng. Q., 8: 125-127.
S. Brandani, V. Brandani / Fluid Phase Equilibria 114 (1996) 37-45
45
Clegg, S.L. and Brimblecombe, P., 1990. Equilibrium partial pressures and mean activity and osmotic coefficients of 0-100% nitric acid as a function of temperature. J. Phys. Chem., 94: 5369-5380. Perry, R.W. and Chilton, C.W., 1973. Chemical Engineer's Handbook 5th Ed., McGraw Hill, New York, pp. 3-60, 3-61. Pitzer, K.S., 1991. Activity Coefficients in Electrolyte Solutions 2nd Edn., CRC Press, Boca Raton, FL. Saul, A. and Wagner, W., 1987. International equations for the saturation properties of ordinary water substance. J. Phys. Chem. Ref. Data, 16: 893-901. Tang, I.N., Munkelwitz, H.R. and Lee, J.H., 1988. Vapor-liquid equilibrium measurements for dilute nitric acid solutions. Atmos. Environ., 22: 2579-2585, TRC Thermodynamic Tables, 1987. Thermodynamic Research Center, Texas A and M University System, College Station, Vol. IV, pp. 500.
Fluid Phase Equilibria 114 (1996) 37-45
Vapor-liquid equilibrium calculation of the system water-nitric acid over the entire concentration range Stefano Brandani *, V i n c e n z o Brandani Dipartimento di Chimica, lngegneria Chimica e Materiali, Universith de L'Aquila, 1-67040 Monteluco di Roio, L'Aquila. Italy Received 1 February 1995; accepted 29 June 1995
Abstract
The vapor-liquid equilibrium of the system water-nitric acid has been described. The activity coefficients in the liquid phase are evaluated according to a new model. This model combines the effect of the long range forces expressed by a Debye-Hi~ckel contribution on a mole fraction basis, with the effect of short range forces expressed by a virial expansion of the NRTL equation. The proposed model can be used to describe the vapor-liquid equilibrium of the system water-nitric acid from 20 to 120 °C over the entire concentration range. Keywords: Theory; Application; Activity coefficients; Nitric acid
1. I n t r o d u c t i o n
The system water-nitric acid is important in industrial applications and environmental control (Tang et al., 1988). There is a considerable interest in the solubility of volatile strong electrolytes in atmospheric clouds and aerosol. Trace quantities of nitric acid are present in the atmosphere as a result of NO x oxidation. For this reason a model for the calculation of vapor-liquid equilibrium has to be capable of describing this system from the infinite dilution region to the pure liquid electrolyte. Clegg and Brimblecombe (1990) have shown that it is not necessary to introduce partial association even at high concentration of the electrolyte. A molal based extended Pitzer model can be applied up to a mole fraction of 0.3 (Brandani et al., 1994). To represent the entire concentration range it is necessary to use model based on mole fraction. Clegg and Brimblecombe (1990) have applied the mole fraction Pitzer model (Pitzer, 1991) up to a mole fraction of approximately 0.5. They have also proposed an extended model which covers the entire concentration range.
* Corresponding author. 0378-3812/96/Sl5.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0 3 7 8 - 3 8 1 2 ( 9 5 ) 0 2 8 1 8 - 8
38
S. Brandani, V. Brandani / Fluid Phase Equilibria 114 (1996) 37-45
In this contribution we propose a new model which retains Pitzer's expression for the Debye-Htickel effect and describes the short range interactions using the VNRTL55 model (Brandani et al., 1991).
2. Activity coefficients model Assuming complete dissociation of the electrolyte, the activity coefficient of the solvent and the mean activity coefficient of the acid are given by: In y, = (In "yl) DH
"t"
(ln
(l)
")/1) SR
In T+*= (ln y +, )~DH + (ln7_+) . SR
(2)
where according to Pitzer ( 1991 )
)DH (lny I
1)/2
=2Axl+pi~/2
2 (In Y_+) , , D n = _ a x P In(1 +
(3)
pilx/2) +
Ilx/2 - 2Ix~/z ] i +P/x--~
(4)
with
(5) p = 2287.66 - ~ I
(6)
2
(7)
I x = 7 . ~ z i Xi
where dw is the density of water (g cm-3). For the short range contribution we propose the use of the VNRTL55 equation (Brandani et al., 1991). This equation gives the activity coefficients from a virial expansion of the NRTL model about their infinite dilution values. Since the structure of the equation is in the form of a virial expansion, it can be easily applied to the water-nitric acid system. Therefore: (lnyl) sR=(lny;)sR+
5(1)
~ j=
5(1) Dj+x~
( l n y 2 ) sR= E j=l
~
~-" Dj, x i
(8)
(9)
S. Brandani, V. Brandani / Fluid Phase Equilibria 114 (1996) 37-45
39
where XH20
X1
(10)
XH~o + 2 XHNO3 (11)
XHNO"
X ±=
XH2O ~ 2XHNO~
where XHNO3 and XH20 are the apparent mole fractions of the electrolyte and water. Djj and Dj+ are the virial expansion coefficients which are dependent only on the NRTL model parameters. The analytical expressions for the first three coefficients are given by Brandani et al. (1991). The last two coefficients in the virial expansions are obtained imposing the boundary conditions. For the solvent the following equations are obtained: (lnYl) s~ + ~ j=
EJ
Dj, = 0
(12)
Dj,=0
(13)
i= while from the mean activity coefficient of the strong electrolyte the following equations can be derived: (In ~'sR + g5 ( 1 )
ln2=0
(14)
j=l
(15)
J7
i--t ~
3. V a p o r - l i q u i d equilibrium calculations
The vapor-liquid equilibrium for the water-nitric system acid is described by the following relationships: P,,~o =
"Y,xlpS~o
(16)
PItNO., = 'y+*2 X±/'/HNO3 2 ,,
(17)
with the assumption of ideal behavior in the vapor phase. The vapor pressure of pure water is taken from Saul and Wagner (1987), while the expression for the Henry constant of nitric acid is taken from Clegg and Brimblecombe (1990) and is given by: In HHNo,(bar) = -- 385.959036 +
3020.3522 T + 71.001998 In T - 0.131442311T
+ 0.420928363 • 10 -4 T 2
(18)
40
S. Brandani, V. Brandani/Fluid Phase Equilibria 114 (1996)37-45
The adjustable parameters in the model are the infinite dilution activity coefficients of the short range contribution, the two interaction parameters and the nonrandomness parameter. The temperature dependence of the first four parameters is obtained from thermodynamic considerations and is given by: (In y]c)SR = a0 + a,
(In
,y~_+)SR ~-
(1 1) T
b0 + bt T
r~+-=c°+cl
~'+-l -= d°-I- dl
T
(,
(19)
TO
(20)
TO
(21)
To
1)
T
(22)
To
Because of the physical meaning of the nonrandomness parameter a , we can suppose it to be a slowly increasing function of temperature. We have assumed a simple linear dependence given by: ,~ = 0.3 + f l ( T - To)
(23)
where TO = 298.15 K.
4. Results and discussion In order to determine the model parameters we have used the experimental isobaric data reported by Boublik and Kuchynka (1960). The measurements are at five different pressure levels 50, 100, 200, 400 and 760 Torr and vary from 24.6 to 120.6 °C over the entire concentration range. The objective function was defined as: N ~SQ
=
Y'. (Ti,ex p -
i=l
N Ti,ca,c)2 + W
Y'~ ( Y i . e x p - Yi,calc) 2
i=l
where N = 68 represents the number of experimental points and W, the ratio o-v2/O-y2, was set to 4- 10 4.
Table I Model parameters ao
-- 1.84___0.05
a1 bo b1 co c1 do dI fl × 104
- 1036+76 -3.12+0.02 - 1976+39 3.35 ___0.09 1189+31 - 2.88 _+ 0.05 - 1316_+41 25.5 + 3.6
S. Brandani, V. Brandani/Fluid Phase Equilihria 114 (1996)37-45
41
I-.-
I 2801 0.0
0.2
0.4
__ 06
_
_ 0.8
1.0
Mole fraction of nitric acid, x,y
Fig. I. Isobaric vapor-liquid equilibria for the system water-nitric acid. - - , calculated, experimental data: A, 50 Torr; *, 100 Torr; m, 200 Torr; x , 400 Tom D, 760 Torr (Boublik and Kuchynka, 1960).
The values of the parameters are reported in Table 1. The model is capable of representing the experimental data with an average absolute deviation (AAD) of 0.76 K on temperature and 0.013 on vapor composition. Fig. 1 shows the comparison between the isobaric experimental data (Boublik and Kuchynka, 1960) and model calculations. Fig. 2 shows the comparison between the isothermal experimental data (Perry and Chilton, 1973) and model calculations at three different isotherms. From these figures it can be seen that there is a very good agreement between the model calculations and the experimental data of Boublik and Kuchynka (1960), while the comparison with the data reported by Perry and Chilton (1973) can be considered satisfactory. The model accurately represents the azeotropic points.
700
~-
/ I
1
10o 0----0
02
04
0.6
0.8
I
Mote fractionof nitricacid, x,y Fig. 2. Isothermal vapor-liquid equilibria for the system water-nitric acid. - - , 25°C; g , 50°C; m, 75°C (Perry and Chilton, 1973).
calculated, experimental data: A,
42
S. Brandani, V. Brandani / Fluid Phase Equilibria 114 (1996) 37-45
1000 0
cl
IO0
el"
~/. 6"""~;J,'6"'"2Jd6"~;~'""3;65""~J:F6""~J4iS~;~5""~.8o
1000/T Fig. 3. Vapor pressure of pure nitric acid as a function of temperature. - - , present model; ---, Clegg and Brimblecombe (1990); D, Perry and Chilton (1973); zx, TRC Thermodynamic Tables (1987).
For the isothermal data, the largest deviations between experimental and calculated values occur at higher concentrations (XHNO3 > 0.7) and at higher temperatures. Since the accuracy of the experimental data reported by Perry and Chilton (1973) is not established, such deviations could be due to experimental uncertainty. In order to check the validity of this statement we carried out a comparison between vapor pressures of pure nitric acid calculated according to our model and those reported by Perry and Chilton (1973) and the more recent data of TRC Thermodynamic Tables (1987). Fig. 3 shows this comparison along with the vapor pressures calculated according to the model of Clegg and Brimblecombe (1990). It can be seen that especially at higher temperatures our model slightly overestimates the vapor pressures reported by TRC Thermodynamic Tables (1987), while there is a larger deviation with the data reported by Perry and Chilton (1973). Taking into account that even very small amounts of water will considerably lower the apparent vapor pressure of nitric acid, we consider the result obtained with our model to be acceptable. The predictions at higher temperatures obtained with the model of Clegg and Brimblecombe (1990) appear to be low, this can probably be ascribed to the fact that their model can be applied over a wider temperature range ( - 60-120 °C). Since Clegg and Brimblecombe (1990) have studied in detail the system water-nitric acid, we have carried out a comparison with their model on the vapor-liquid equilibrium calculations. Clegg and Brimblecombe (1990) use an extension of the model proposed by Pitzer (1991) to describe the entire concentration range. An explicit temperature dependence of the model parameters is not given. To obtain this information the activity coefficients are first evaluated at a reference temperature (25 °C) and then the solute and solvent activities can be calculated at any given temperature using the partial molal enthalpies and the partial molal heat capacities. The partial molal enthalpies are calculated using four sets of Chebyshev polynomials corresponding to four concentration intervals, while the partial molal heat capacities are expressed in the form of three sets of Chebyshev polynomials corresponding to three concentration intervals. The overall computational scheme is therefore more cumbersome. The model has been correlated to an extensive data base fitting 4 parameters at 25 °C
43
S. Brandani, V. Brandani / Fluid Phase Equilibria 114 (1996)37-45
Table 2 Comparison of differentmodels on isobaric experimental data (Boublik and Kuchynka, 1960)
Present model Clegg and Brimblecombe(1990)
AAD (68) a 7"(K)
y
0.76 2,90
0.013 0.035
Value in parenthesis is the number of data points.
Table 3 Comparison of differentmodels on isothermalexperimental data
Present model Clegg and Brimblecombe(1990)
Perry and Chilton(1973) AAD (Tort) Pn:o (260) a PHNO3 (260) a 5.81 7.89 6.98 10.9
Tang et al. (1988) AAD (Torr) P"2o (9) a PHNO3 (22) a 0.578 0.00113 0,027 0.00013
a Values in parenthesis are the number of data points. and a total of 96 coefficients of the Chebyshev polynomials. For this reason the Clegg and Brimblecombe model can be considered highly accurate. Table 2 reports the comparison between the two models applied to the isobaric experimental data of Boublik and Kuchynka (1960). Table 3 reports the comparison between the two models with the isothermal data given by Perry and Chilton (1973) and by Tang et al. (1988). The comparison shows that our model represents the system water-nitric acid over the entire concentration range with an accuracy comparable to that of Clegg and Brimblecombe (1990). The data of Tang et al. (1988) which are at low acid compositions (XHyo3 < 0.11) show that our model is less accurate in the dilute region. If very accurate evaluations are needed in this range of compositions either the Clegg and Brimblecombe model or the model of Brandani et al. (1994) should be used.
5. Conclusion We have presented a new model capable of representing the vapor-liquid equilibrium of the system water-nitric acid over the entire concentration range. An explicit temperature dependence has been given for each adjustable parameter which allows the vapor-liquid equilibrium calculations over the temperature range 20-120°C. For practical applications this model is more easily coded and has a simpler computational scheme than the model proposed by Clegg and Brimblecombe (1990).
6. List of symbols Ax dw
parameter defined by Eq. 5 density of water
44
S. Brandani. V. Brandani / Fluid Phase Equilibria 114 (1996) 37-45
Djl Dj + e
H Ix k
NA PHNO) °
T W x
Y
virial coefficients of the solvent virial coefficients of the mean activity coefficient electric charge Henry's constant ionic strength defined in Eq. 7 Boltzmann's constant Avogadro's number partial pressure of nitric acid partial pressure of water vapor pressure of pure component temperature weight in objective function (Eq. 24) mole fraction in the liquid phase mole fraction in the vapor phase
6.1.1. Greek letters o/ nonrandomness parameter activity coefficient of water Yl mean activity coefficient 3'_+ dielectric constant of water E parameter defined by Eq. 6 P interaction parameter of the NRTL equation ~u 6.1.2. Superscripts and subscripts DH Debye-HiJckel contribution HNO 3 nitric acid H 2° water SR short range contribution
Acknowledgements The authors are indebted to the italian Ministero dell'Universith e della Ricerca Scientifica e Tecnologica (MURST) for financial support.
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